Supersymmetric black holes and attractors in gauged supergravity with hypermultiplets

We consider four-dimensional N = 2 supergravity coupled to vector-and hypermultiplets, where abelian isometries of the quaternionic Kahler hypermultiplet scalar manifold are gauged. Using the recipe given by Meessen and Ortin in arXiv:1204.0493, we analytically construct a supersymmetric black hole solution for the case of just one vector multiplet with prepotential F = -i chi(0)chi(1), and the universal hypermultiplet. This solution has a running dilaton, and it interpolates between AdS(2) x H-2 at the horizon and a hyperscaling-violating type geometry at infinity, conformal to AdS(2) x H-2. It carries two magnetic charges that are completely fixed in terms of the parameters that appear in the Killing vector used for the gauging. In the second part of the paper, we extend the work of Bellucci et al. on black hole attractors in gauged supergravity to the case where also hypermultiplets are present. The attractors are shown to be governed by an effective potential V-eff, which is extremized on the horizon by all the scalar fields of the theory. Moreover, the entropy is given by the critical value of V-eff. In the limit of vanishing scalar potential, V-eff reduces (up to a prefactor) to the usual black hole potential.